Integrating factor for a particular equation

Question

what would be the integrating factor for:

$$\frac{dy}{dx}-4y=e^{4x}\cosh^23x$$

Would it be $4x$? Thank You.

Answer 1

No, it would not be $4x$.

If you have a differential equation in the form

$$\frac{dy}{dx} +p(x)y = q(x)$$

the integrating factor is $I(x) = \exp(\int p(x)dx)$. In your case, $p(x) = -4$ so $I(x) = \exp(\int -4 dx)$. Can you take it from here?